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Beliebt Rechnen >

(\partial)/(\partial y)(4xy-x^4-y^4)

Lösung

\frac{\partial}{\partial y} (4 x y - x^{4} - y^{4})

Lösung

4 x - 4 y^{3}

Schritte zur Lösung

\frac{\partial}{\partial y} (4 x y - x^{4} - y^{4})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (4 x y) - \frac{\partial}{\partial y} (x^{4}) - \frac{\partial}{\partial y} (y^{4})

\frac{\partial}{\partial y} (4 x y) = 4 x

\frac{\partial}{\partial y} (x^{4}) = 0

\frac{\partial}{\partial y} (y^{4}) = 4 y^{3}

= 4 x - 0 - 4 y^{3}

Vereinfache

= 4 x - 4 y^{3}

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